Question

Resolva as equações do 2° grau a)x²+x•(2x-45)=0 b) (x-7)•(x-3)+10x=0 b) x+5=20/x+4 c) (4+3x)² - 24x=52

Answer 1

a) xx ( x + 2 x - 45) = 0

xx ( x + 2 x - 45) = 0

x ( 3x - 45 ) = 0

x 3( x - 15 ) = 0

x ( x - 15) = 0

x = 0 

x = 15

x1 = 0 , x² = 15

b) x² - 3x - 7 x + 21 + 18 x = 0

x² + 8 x + 21 = 0

x =  - 8 ± √8²- 4 x 1 x21
---------------------------------
               2x1

x = -8± √64 - 84
---------------------------
          2

x = - 8 ± √ - 20
--------------------
      2

X ∉ R

c) x+5=20/x+4

x + 5 = 20/x + 4 , x ≠ 0

x + 5 - 20/x - 4 =0

x + 1 - 20/x = 0

x² + x - 20 = 0

x = -1             ±  √ 1² - 4 x1 x ( - 20 )
                     ------------------------------------
                                2x1

x = - 1  ± √ 1 + 80
          ---------------------
               2

x =  - 1  ± √81
      ---------------------
            2

x = -1  ± 9
     ----------
           2
         
x = 4 

x = -5      , x≠ 0


x = 4 

x = -5 

x1 = -5 , x²  = 4

Answer 2

a) X²+X.(2X-45)=0
x² + 2x² - 45x = 0
3x² - 45x = 0 ÷ 3
x² - 15x = 0
x.(x - 15) = 0
x = 0
x - 15 = 0
x = +15 

b)(x-7)(x-3)+10x=30
x^2-3x-7x+21+10x=30
x^2-10x+10x=30-21
x^2=30-21
x^2=9
x= raiz de 9
x=-/+ 3
S[0 ; 15]

c)
(4+3x)²-24x=54
9x²+2·4·3x+16-24x-54=0
9x²+24x+16-24x-54=0
9x²-38=0
x²=38/9
x=√38/9
x=6√1